Method of locating a fault in a predetermined monitoring region of a multiphase electric power transmission system

ABSTRACT

A method for locating a fault in an electric power transmission line to form measured precursor fault vector values of two aerial modes from sample values from currents and voltages stored immediately before and during an occurrence of the fault, using the Clarke transformation. For synchronization, the phase angle is determined from these measured vector values, so that fault vector voltage values of both aerial modes can be generated without distortion by asynchronously forming the sample values. The fault vector voltage values of one aerial mode are subtracted from those of the other aerial mode, and the resulting differences are squared. The location of the fault is determined by estimating the minimum value of the sum of the squared differences.

It is general knowledge that a predetermined region of an electric powertransmission line system, e.g., a section of a three-phase powertransmission line, can be monitored for faults by providing a protectivedevice at each end of the section of electric power transmission line.Each protective device is generally provided with a fault detectorcircuit that delivers a signal to activate the respective protectivedevice when a fault occurs.

It is also known ("New accurate transmission line fault locationequipment," IEE Conf. Publ. 302, 1989, pages 1-5) that currents andvoltages can be stored at each end of a section of a multiphase electricpower transmission line to be monitored in a method of locating a fault,where this is accomplished by determining values immediately before andduring the occurrence of a fault. The stored values are sampled andprocessed further in different ways, depending on whether they areassigned to values stored before or during a fault.

As also stated in IEE Proceedings, vol. 137, pt. C, no. 6, November1990, pages 395-402, for accurate location of a fault in a three-phasepower transmission line by this known method, variables obtained byusing the known Clarke transformation in the transition to modal valuesor functions are taken into account. At each end of a section of anelectric power transmission line to be monitored, first the sampledvalues obtained from currents and voltages stored immediately before afault occurs are taken into account, and measured precursor fault vectorvalues of one aerial mode are formed from these sample values. Theaerial mode is a mode which, in addition to another aerial mode and aground-based mode is characteristic of the Clarke transformation. Usingthe measured precursor fault vector values, a phase angle is determinedon the basis of asynchronous sampling at the two ends of the section ofthe power transmission line to be monitored between the measuredprecursor fault vector values. In the known method, which takes intoaccount sample values calculated from currents and voltages storedduring the fault, fault vector voltage values are calculated using themeasured precursor fault vector values, with intermediate calculation ofdifferential measured vector values; these fault vector voltage valuesare measured values indicating the voltage at the fault location, asconsidered in relation to both ends of the section of electric powertransmission line to be monitored. Since the fault vector voltage valuesdetermined from both sides for the same fault location must be the same,this yields the possibility of calculating the location of the faultwith a relatively high accuracy. However, the prerequisite is that thephases of the two fault vector voltage values must match. Since this isnot the case with the known method, the phase angle is determined withthe measured precursor fault vector values and a corresponding measuredphase angle value is formed. This measured value is used forsynchronization of the fault vector voltage values and only then is thelocation of the fault determined from the fault vector voltage values.

The known method is subject to some uncertainty in locating a faultinasmuch as complete diagonalization is impossible with a Clarketransformation. This is where the invention begins, by formulating theobject of providing a method of locating a fault in a predeterminedregion of a multiphase electric power transmission line system with anespecially high measurement accuracy.

This object is achieved according to this invention in a method oflocating a fault in a predetermined monitoring region of a multiphaseelectric power transmission line system with the detection of voltagesand currents of the phase conductors at the ends of the monitoringregion, where measured values that are proportional to the currents andvoltages and occur immediately before and during the fault at the endsof each monitoring region are stored; measured precursor fault vectorvalues of one aerial mode and another aerial mode are formed by Clarketransformation from sample values formed from voltages and currentsstored immediately before the occurrence of a fault; the measuredprecursor fault vector values of the different ends of the monitoringregion are tested for their phase angle relative to each other and ameasured phase angle value corresponding to the phase angle is formed;furthermore, fault vector voltage values of one aerial mode and theother aerial mode are formed from sample values obtained from currentsand voltages stored when a fault occurs, taking into account themeasured precursor fault vector values, and the fault vector voltagevalues of the one aerial mode are subtracted from those of the other,and the resulting differences are squared, and then the location of thefault is determined from an estimated minimum value of the sum of thesquared differences.

The basic advantage of the method according to this invention is that byusing the additional measured precursor fault vector values of anadditional aerial mode in this method and the additional fault vectorvoltage values of the same additional aerial mode, it is possible tolocate the fault by means of an estimate according to the least squarescriterion, so the location of the fault can be determined with acomparatively high accuracy.

In the method according to this invention, deriving an accurate measuredphase angle value is especially important because the measurementaccuracy of the method according to this invention also depends onaccurate determination of measured phase angle values. This is takeninto account in an advantageous embodiment of the method according tothis invention, whereby to obtain the measured phase angle value,precursor fault vector voltage values and precursor fault vector currentvalues are formed from both aerial modes, the paired precursor faultvector voltage values and precursor fault vector current values of oneaerial mode are subtracted from those of the other aerial mode, theresulting differences are squared, and the measured phase angle value isdetermined from an estimated minimum value for the sum of the squareddifferences.

The advantage of this embodiment of the method according to thisinvention is that differences are formed using not only precursor faultvector voltage values but also precursor fault vector current values,and after squaring these differences, they are also analyzed accordingto the least squares criterion, so the measured phase angle value can bedetermined with a high accuracy.

To further illustrate this invention:

FIG. 1 shows a three-phase power transmission line with a section to bemonitored;

FIG. 2 shows a type of block schematic to illustrate the sequence in themethod according to this invention;

FIG. 3 shows a vector diagram to illustrate how the measured phase anglevalue is determined when voltage is taken into account;

FIG. 4 shows a vector diagram corresponding to FIG. 3 where current istaken into account; and

FIG. 5 shows the region of a power transmission line to be monitoredwith a fault.

According to FIG. 1, an electric power transmission line E has threephase conductors A, B and C. The electric power transmission line Eextends between one end S and another end R. It has length L. At eachend S and R of electric power transmission line E there is a protectivedevice SE1 and SE2 that receives the currents in conductors A through Cand the voltages on these phase conductors in a manner only indicatedschematically here.

Each protective device SE1 and SE2 contains, e.g., a distance protectiondevice (not shown) with a fault detector circuit (also not shown).Furthermore, each protective device SE1 and SE2 is equipped with adevice (not shown in FIG. 1) for recording the currents in phaseconductors A, B and C and the voltages in these phase conductors ofelectric power transmission line E.

As FIG. 2 shows, downstream from each of these devices E1 and E2(diagramed only schematically) is a weighting network BW1 and BW2 torecord the currents and voltages and receive sample values AW1 and AW2after a fault occurs. Sample values AW1 and AW2 are formed by samplingthe variations in the currents and voltages in conductors A through C ofelectric power transmission line E recorded immediately before andduring a fault. Taking into account the known Clarke transformation,measured precursor fault vector values V_(BF),m^(S) and I_(BF),m^(S) aswell as V_(BF),m^(R),async and I_(BF),m^(R),async are formed inweighting networks BW1 and BW2 as voltage- and current-based measuredprecursor fault vector values from sample values obtained immediatelybefore a fault occurs. In this notation, m denotes one aerial mode (α)or the other aerial mode (β) according to Clarke transformation. Theletters S and R denote the respective ends of the power transmissionline, while async indicates that the measured precursor fault vectorvalues assigned to end R have not been synchronized with those of end S.

The resulting precursor fault measured values V_(BF),m^(S) andI_(BF),m^(S) as well as V_(BF),m^(R),async and I_(BF),m^(R),async aresent to an estimator SG where a measured phase angle value PM isdetermined. In this estimator SG, currents I_(m) ^(S) and I_(m) ^(R) aswell as voltages V_(m) ^(S) and V_(m) ^(R) "coming" from the two ends Sand R or from protective devices SE1 and SE2 and occurring at half thelength L/2 of the line section monitored are calculated with themeasured precursor fault vector values. These values can be described bythe following equations: ##EQU1##

Since the currents and voltages must be the same at the assumed middleof the region of the power transmission line E to be monitored, thefollowing equation (5) can be formulated for the voltages: ##EQU2##

A similar relation can be formulated for the currents, as shown by thefollowing equation (6): ##EQU3##

In equations (1) through (6), Zc_(m) denotes the modal line impedanceand γ_(m) denotes the modal propagation constant according to the Clarketransformation; δ denotes the phase angle between paired measuredprecursor fault vector values. The variables ε_(V).sbsb.m andε_(I).sbsb.m are fault variables. FIG. 3 illustrates the individualvariables for the voltage relationships, and FIG. 4 shows the currentrelationships in graphic form.

To determine phase angle δ and measured phase angle value PM, thedifferences ε_(V).sbsb.m and ε_(I).sbsb.m are squared for both aerialmodes α and β, yielding a one-dimensional cost function K_(f) accordingto the following equation (7): ##EQU4##

According to the least squares criterion, the cost function K_(f) isminimized using the simplex method, which yields phase angle δ andmeasured phase angle value PM. The line parameters are supplied by blockLP.

In addition to the measured precursor fault vector values, differentialmeasured vector values V_(SUP),m^(S) and V_(SUP),m^(R),async as well asI_(SUP),m^(S) and I_(SUP),m^(R),async according to both aerial modes αand β are formed by generating the difference between one measuredvector value derived from sample values formed from voltages andcurrents stored during the fault (in both aerial modes) and therespective measured precursor fault vector values. Then the phases ofthe differential measured vector values formed by weighting network BW2from the values at line end R are rotated according to the measuredphase angle δ in an intermediate arrangement ZA; for this purpose,intermediate arrangement ZA receives measured phase angle value PM.Measured values V_(SUP),m^(R) and I_(SUP),m^(R) appear at the output ofthe intermediate arrangement.

Consequently, analyzing unit AS downstream from intermediate circuit ZAis supplied with differential measured vector values V_(SUP),m^(R) andI_(SUP),m^(R) which are synchronized with differential measured vectorvalues V_(SUP),m^(S) and I_(SUP),m^(S) of weighting network BW1; thisunit uses these differential measured vector values to form fault vectorvoltage values V_(SUP),m^(FfromS), V_(SUP),m^(FfromR) from the two endsS and R according to equations (8) and (9): ##EQU5##

Paired fault vector voltage values of one aerial mode α or β aresubtracted from those one another, forming differences ε_(V).sbsb.m,SUPaccording to the following equation (10): ##EQU6##

A one-dimensional cost function K is formed from the squares of thedifferences according to equation (11) below, which is analyzedaccording to the least error squares criterion. ##EQU7##

Then the position x of a fault F on transmission line E can bedetermined with a high accuracy (see FIG. 5).

Equations (8) and (9) describe the relationships approximately. In anaccurate analysis with partial coupling compensation, the followingequation (12), for example, is obtained for the fault vector voltagevalue V_(SUP),m^(FfromS) : ##EQU8##

In this equation (12), m denotes one aerial mode and m' denotes theother aerial mode; j·M_(m),0 ·x denotes the reactance between themeasurement location and the fault location, while equ indicates thatthe current is integrated from the measurement location to the faultlocation.

The fault vector voltage values corrected in this way are analyzedaccording to equations (10) and (11).

A further increase in accuracy in locating a fault can be achieved withthe method according to this invention by performing a fault estimatewith regard to the inductances of the power transmission line. In thiscase, predetermined inductance values per unit of length of powertransmission line are assumed, and the fact that the cost functionaccording to equation (7) now depends not only on phase angle δ but alsoon inductance values l_(m), where m=α or β according to Clarketransformation of the power transmission line, is also taken intoaccount. Again in this case, a minimization is performed according tothe simplex method, beginning with the solution for phase angle δ andthe predetermined inductance values.

Once l_(m) has been determined, the variables Zc_(m) and γ_(m) can bedetermined according to the following equations (13) and (14): ##EQU9##where r_(m) and c_(m) denote, respectively, the resistive and capacitiveline parameters per unit of length according to Clarke. The valuesZc_(m) and γ_(m) thus obtained are entered into equations (8) and (9)and then location x of fault F is determined accurately according toequations (10) and (11).

What is claimed is:
 1. A method for locating a fault in a predeterminedmonitoring region of a multiphase electric power transmission linesystem, the method comprising the steps of:measuring first currents andvoltages of phase conductors at end sections of the predeterminedmonitoring region, the measured first currents and voltages occuringimmediately before and during the fault; storing first measured valuesproportional to the measured first currents and voltages; forming firstsampled values according to a Clarke transformation immediately beforethe fault occurs; forming measured precursor fault vector values of afirst aerial mode and of a second aerial mode as a function of thesampled values for each of the ends of the predetermined monitoringregion; testing the measured precursor fault vector values of the endsof the predetermined monitoring region; determining a measured phaseangle value by:(a) forming second currents and voltages occurring atapproximately a midpoint of the predetermined monitoring region as afunction of the measured precursor fault vector values for the firstaerial mode, (b) forming third currents and voltages occurring atapproximately a midpoint of the predetermined monitoring region as afunction of the measured precursor fault vector value for the secondaerial mode, (c) subtracting the second currents and voltages from thethird currents and voltages to generate first resultant differences, (d)squaring the first resulting differences, and (e) obtaining the measuredphase angle value as a function of a first estimated minimum value of asum of the squared first resultant differences, forming voltage-basedand current-based differential measured vector values that aresynchronized for each of the first and second aerial modes and for eachend of the predetermined monitoring region as a function of the samplevalues, the measured phase angle values and the measured secondprecursor fault vector values; determining a first fault vector voltagevalue as a function of the synchronized differential measured vectorvalues for the first aerial mode and for each of the two ends of thepredetermined monitoring region; determining a second fault vectorvoltage value as a function of the synchronized differential measuredvector values for the second aerial mode and for each of the two ends ofthe predetermined monitoring region; subtracting the first fault vectorvoltage value from the second fault vector voltage value to providesecond resulting differences; squaring the second resulting differences;and determining the location of the fault as a function of a secondestimated minimum of the sum of the squared second resultingdifferences.
 2. The method according to claim 1, further comprising thestep of:after the step of determining the measured phase angle value,estimating measured inductance values of the first and second aerialmodes as a function of predetermined inductance values of the powertransmission system, wherein the first and second fault vector voltagevalues are determined as a further function of the measured inductancevalues.